Derivate-free methods for unconstrained nonsmooth optimization and its numerical analysis

Numerical algorithms for solving the unconstrained problems of Lipschitz optimization are presented. These algorithms are based on continuous approximations to the subdifferential and belong to the numerical algorithms of nonsmooth optimization without calculating derivatives. We give a definition of such approximations and propose a method for its construction. An algorithm for the computation of descent direction of the objective function is described. We consider various procedures for the computation of stepsize. The results of numerical experiments are presented. We compare the suggested algorithms using these results.